Page 563 - Petrophysics

530 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Using Darcy's law (for qt) and Poiseuille's law (for % and sf) gives:

(8.62)

The total area of matrix and fracture can be expressed as:

(8.63)

Assuming equal storage capacity of both systems (matrix and fracture),
i.e., the porosity partitioning coefficient v is approximately 0.50 and
therefore n, = nf and @f = Qc, Equation 8.63 simplifies as:

At = (nr: + hfwf) (8.64)

Thus the average permeability can be extracted first by substituting
Equation 8.64 in 8.62 and then solving for k:

(8.65)

For a unit block area, hf = 1. While hf and wf can be relatively easily
measured, this is not always the case with rc. A rather simplistic approach
to determine average permeability in type 2 reservoirs is to calculate the
geometric mean of the two systems:

(8.66)

Assuming the average porosity @ = Equation 8.66 becomes:

It is obvious from this discussion that in naturally fractured carbonate
formations, where structural heterogeneities and textural changes are
common and only a small number of wells are cored, the practice of using
statistical core permeability-porosity relations to characterize flow units
is not recommended. The main parameters that influence the flow units
in naturally fractured reservoirs include: secondary porosity (fractures,